2,5D DC Resistivity Modeling Considering Flexibility And Accuracy_ppt.pdf

7/29/2019 2,5D DC Resistivity Modeling Considering Flexibility And Accuracy_ppt.pdf

1/15

2.5-D DC Resistivity Modeling ConsideringFlexibility and Accuracy

Okto Ivansyah

22311008

Dosen:

Prof. Dr. Wawan Gunawan A. Kadir, MS.

Teknik Geofisika FTTM ITB, Bandung 2012

Journal of Earth Science, Vol. 22, No. 1, p. 124130, February2011Printed in ChinaDOI: 10.1007/s12583-011-0163-z

Tang Jingtian (), Wang Feiyan* (), Xiao Xiao (), Zhang Lincheng ()


2/15

Outline

IntroductionBoundary Value Problem

2.5D DC Resistivity Modeling By

Adaptive Finite-Element MethodeAccuracy And Flexibility Testing

An Enhanced Technique For Accuracy

Conclusion


3/15

Introduction

2.5D DC Simulation

2.5-D DC modeling by the finite-element

approaches

Main attention is focused on a specificclass of layered models which own a high

conductivity contrast.


4/15

Boundary Value Problem

Assume that the strike direction is along the z-axis in the Cartesian coordinatesystem, then the 2.5-D boundary value problem due to single source point can be

obtained by Fourier transform:

(1)

where is the Dirac delta function; (x, y) denotes the conductivitydistribution; nmeans the outward normal vector; K0(kr) and K1(kr)respectively denote the modified Bessel function of the first kind

zero order and the first kind first order; ris the vector pointing from

the source point to arbitrary location on the truncated boundary

which is usually extended far enough to improve the accuracy;


5/15


Then, U(x, y) is the transformed potential in the wavenumber domain whichcan be obtained by the cosine-Fourier transform

(2)

where kdenotes the wavenumber computed by the optimal algorithm (Xu etal., 2000); u(x, y, z) is the total potential.


6/15


The total potential could be recovered by the discrete inverse Fourier

transform

(3)

where gi is the weighted coefficient corresponding to the ith wavenumber; Nkdenotes the total number of the discrete wavenumbers.


7/15


Adaptive Finite-Element Methode

According to the error estimator, the L2-norm element-wise error can be

expressed as

(4)

where dU* denotes the recovered gradient (Zienkiewicz and Taylor,2000); Uhmeans the gradient of the finite-element solution in thecurrent mesh; neis the total number of elements.


8/15


Adaptive Finite-Element Methode

Through a summation, the global error estimator can be written into

(5)

Then the new element size for the next new mesh can be predicted like (Tang et

al., 2010)

(6)


9/15

Accuracy And Flexibility Testing

Figure 1. (a) Relative errors of the apparent resistivities calculated from iteratively generated meshes;(b) two-layered model; (c) initial mesh (322 nodes); (d) final mesh (5 798 nodes).

Model 1


10/15

Accuracy And Flexibility Testing

Model 2

Figure 2. (a) Final mesh discretization when the dipole source locates as shown in this figure; (b)

anomalies due to the rugged topography; (c) anomalies over a rectangular inhomogeneity withtopography included; (d) anomalies after correction of topography.


11/15

An Enhanced Technique ForAccuracy

To solve the problem, we utilize the layered earth as the reference model tocalculate the enhanced wavenumbers and mixed boundary condition. Here, we

take a horizontally twolayered model to show the accuracy of the new algorithm.

Then, the analytical expression (Li, 2005)


12/15


Figure 3. (a) Comparison of apparent resistivities fromdifferent techniques; (b) two-layered model.

A horizontally two-layered model issimulated to validate what we have

analyzed. The size of the model with

a low resistivity of1=1 m in the

upper layer and 1=100 m in the

underlying earth is 600 m300 m.

Single source point is located at the

original point (see in Fig. 3b). The

pole-pole array is performed with a

measuring range from -160 to 160

m. Equally distributed measuring

electrodes with an electrode interval

8 m are deployed.


13/15


Figure 4. (a) Comparison of apparent resistivities from

different techniques; (b) a rectangular inhomogeneityburied in two-layered earth.

Based on the above validation, arectangular inhomogeneity

embedded in the above two-

layered earth is simulated. This

local anomaly has a size of 3

m8 m with a resistivity of 100

m. The background two-

layered structure owns a

thickness of 10 m. The resistivity

of the upper layer is 1 m, and

the underlying earth has a

resistivity of 100 m. Single

source is located at (-15 m, 0)

(see Fig. 4b).


14/15

Conclusion

In contrast to simulating the complex topography in the staircase-like

manner, the unstructured triangular mesh together with the adaptive

refinement makes the simulation much more reasonable. Based on this,

the accuracy problem for some typical layered earth models is analyzed.The enhanced wavenumbers are calculated for the models with large

conductivity contrast. Our study shows that the accuracy has been

obviously improved by using the new algorithm.


15/15

Terima Kasih

2,5D DC Resistivity Modeling Considering Flexibility And Accuracy_ppt.pdf

Documents

Transcript of 2,5D DC Resistivity Modeling Considering Flexibility And Accuracy_ppt.pdf